半参数模型的若干问题探讨

发布时间：2018-10-29 19:56

【摘要】：半参数模型把非参数分量加入观测方程中,一方面使得建立的数学模型与真实情况更为接近,另一方面能在数值上分别求出系统误差和偶然误差的估值。本文探讨了半参数模型的若干问题,讨论了几种传统模型与半参数模型的结合,分析采用补偿最小二乘准则与最小二乘准则的区别,探讨了几种数据处理方法与半参数模型相结合的优点,并用算例验证,传统模型与半参数模型结合得到的参数估值精度明显提高。本文主要内容如下:1.基于半参数模型与补偿最小二乘估计方法,分析了正规矩阵R和平滑因子α的选取方法。对比分析了传统参数模型与半参数模型对于系统误差的稳定性,鉴于传统平滑因子选取方法偏于复杂且计算量大,提出了一种新的更加简便的平滑因子选取方法——基于效率最优准则的平滑因子选取方法。2.研究了基于半参数模型的灰色预测建模方法,并通过改进传统正规矩阵的选取方法,分析不同正规矩阵对参数估值的影响及其精度变化,结合变形监测数据,探讨补偿最小二乘准则下的灰色预测与最小二乘准则下的灰色预测精度的变化。3.对于半参数模型及其岭估计,探讨了当法矩阵病态时模型的解法,探讨了岭参数的选取方法,分析了半参数模型岭估计与泛补偿最小二乘估计之间的联系。通过算例分析了半参数模型与半参数岭估计解算病态模型对参数估值的影响。4.考虑到最小二乘估计不具备抗差性,所以补偿最小二乘估计也不具备抗差性,研究了半参数模型抗差估计,探讨了抗差估计权因子的选取方法,推导了基于选权迭代法的半参数抗差估计的计算公式,通过算例对比分析了几种模型解的精度以及对精度的影响。
[Abstract]:The semi-parametric model adds nonparametric components into the observation equation on the one hand makes the established mathematical model closer to the real situation on the other hand it can numerically calculate the estimates of the system error and the accidental error respectively. This paper discusses some problems of semi-parametric model, discusses the combination of several traditional models and semi-parametric models, and analyzes the differences between the compensatory least square criterion and least square criterion. This paper discusses the advantages of combining several data processing methods with semi-parametric model and verifies by an example that the precision of parameter estimation obtained by combining traditional model with semi-parametric model is obviously improved. The main contents of this paper are as follows: 1. Based on the semi-parametric model and the compensated least square estimation method, the selection method of normal matrix R and smoothing factor 伪 is analyzed. The stability of the system error between the traditional parameter model and the semi-parametric model is compared and analyzed. In view of the complexity of the traditional smoothing factor selection method and the large amount of calculation, In this paper, a new and more convenient method for selecting smoothing factors is proposed, which is based on the optimal efficiency criterion. 2. The grey prediction modeling method based on semi-parametric model is studied. By improving the traditional normal matrix selection method, the influence of different normal matrices on parameter estimation and its accuracy change are analyzed, and the deformation monitoring data are combined. This paper discusses the variation of grey prediction accuracy under the least square criterion and the least square criterion. 3. For the semi-parametric model and its ridge estimation, this paper discusses the solution of the model when the normal matrix is ill-conditioned, discusses the selection method of the ridge parameter, and analyzes the relationship between the semi-parametric model ridge estimation and the universal compensated least square estimation. The effects of semi-parametric model and ill-conditioned model of semi-parametric ridge estimation on parameter estimation are analyzed by an example. 4. Considering that the least square estimation is not robust, so the compensated least squares estimation is not robust, so the robust estimation of semi-parametric model is studied, and the method of selecting the weight factor of robust estimation is discussed. The calculation formula of semi-parameter robust estimation based on weight selection iteration method is derived. The accuracy of several model solutions and their effects on accuracy are analyzed by examples.
【学位授予单位】：东华理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P207

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